Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
338 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#17984760 | C2 | semidirect |
| 4. #22580721 | C2 | semidirect |
| 88. C22×C139 | #101 | semidirect |
| 104. C139 | #1901 | semidirect |
| 193. C22 | #17984760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555769 | 2 |
| C2×#17984821 | 2 |
| C2×#17984760 | 2 |
| #22580721 | 2 |
| #407×C139 | 2 |
| #1901 | 139 |